On this site I have a custom post type called 'listings'. I'd like to have these custom posts added to the dropdown menu in Atahualpa with the parent 'featured listings'. I'm not currently using the custom menu's from the wordpress dashboard. Any advice is appreciated. Thanks!

Atahualpa will only add pages to the menu's. You should look for a plugin that does what you want

Ok, I created a new custom menu through appearance > menus. I can then add my posts manually.

If anybody can recommend a good plugin for automatically adding these posts of a specific category or type, it would be much appreciated.